Althaus, T.

Erk, A.

Hardy, E. H.

Stahl, W.

KITopen

Full PaperFiltration of Colloidal Suspensions – MRIInvestigation and Numerical SimulationThe principle mechanisms of solid-liquid separation processes are sedimentationand filtration, both including the formation and compression of a liquid-satu-rated bulk. The compressive properties of the bulk determine the operating para-meters of solid-liquid separation devices and the achievable separation results. In-formation about the solids volume fraction of the bulk is essential for a better un-derstanding of the physical mechanisms and precise modeling. A numerical mod-el for the calculation of the local solids volume fraction during formation andcompression of filter cakes and sediments was developed. The calculated resultsare compared with experimental NMR data.Keywords: Colloids, Filtration, Nuclear magnetic resonance (NMR), Simulation,SuspensionsReceived: February 3, 2006; accepted: March 17, 2006DOI: 10.1002/ceat.2006000541 IntroductionSolid-liquid separation of fine particulate suspensions is of im-portance in many fields of process technology. Examples in-clude the industrial production of pigments and ceramics suchas titania, alumina, and kaolin, as well as food processing andwastewater treatment. The principle mechanisms of solid-liq-uid separation processes are sedimentation and filtration. Bothcases include the formation and compression of a liquid-satu-rated bulk (sediment or filter cake). The compressive proper-ties of the bulk determine the operating parameters of solid-liquid separation devices and the achievable separation results.The solids volume fraction of the bulk strongly depends onthe local stress. In the transient state a liquid transport withinthe porous system takes place. As a result, a time-dependentgradient of the solids volume fraction develops. Spatially re-solved information about the solids volume fraction as a func-tion of time under different conditions (e.g., pressure, pH) al-lows a better understanding of the physical mechanisms and,thus, more precise modeling. The required data can be gainedby magnetic resonance imaging (MRI) in a nondestructive andhighly resolved way.In this paper, experimental and calculated results concerningsolids volume fraction profiles during the formation and com-pression of fine particulate filter cakes are presented. A numer-ical model for the calculation of the local solids volume frac-tion during formation and compression of filter cakes andsediments was developed. The calculated results are comparedwith the experimental NMR data.This work focuses on the application of a model and a nu-merical simulation program for describing dynamic filtrationprocesses and its validation by means of in situ NMR measure-ments. Further, this research is aimed at gaining a better un-derstanding of the structural changes within fine particulatefilter cakes during their formation and consolidation and at in-vestigating the influence of interparticle forces.The description of dynamic filtration and consolidationprocesses used for this work is based on an approach and a nu-merical algorithm developed by Bürger et al. [1, 2]. In thismodel the material properties are characterized by two materi-al functions: the permeability as a function of the solids vol-ume fraction, k(), on the one hand, and the compressiveyield stress as a function of the solids volume fraction, ps(),on the other hand1).The permeability k determines the hydrodynamic interac-tion between the solid and the liquid phase and, thus, the ki-netics of the fluid transport within the filter cake. The com-pressive yield stress ps is a measure for the strength of aparticle network in compression and determines the equilibri-um solids concentration reached at a certain applied pressure.Furthermore, the fluid viscosity and the density difference be-tween the solid and the liquid phase have to be known.Implementation of the model and the material functions ina numerical simulation program allows the calculation of thelocal solids volume fraction within a filter cake as a function of© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.comAtes Erk1Edme H. Hardy2Tim Althaus3Werner Stahl21BASF AG, Ludwigshafen,Germany.2 Institut für MechanischeVerfahrenstechnik undMechanik, UniversitätKarlsruhe (TH), Germany.3 Institut für Lebensmittel- undErnährungswissenschaften,ETH, Zürich, Switzerland.–Correspondence: Dipl.-Ing. A. Erk (ates.erk@basf.com), BASF AG,GCT/R-L549, D-67056 Ludwigshafen, Germany.–1) List of symbols at the end of the paper.828 Chem. Eng. Technol. 2006, 29, No. 7, 828–831First published in:EVA-STAR (Elektronisches Volltextarchiv – Scientific Articles Repository) http://digbib.ubka.uni-karlsruhe.de/volltexte/1000008769 operating parameters and time. The required data to specifythe filtration process includes the initial solids volume fraction0, the initial suspension mass per unit filtration area, the ap-plied pressure difference Dp and the flow resistance of the filtermedium. The program code used to calculate the resultsshown below was implemented in Matlab 6.5 (The MathworksInc.).For the simulation of the filtration process, the solid-liquid-system is divided into several slices parallel to the plane of thefilter medium. A typical slice thickness used in this study was0.1 mm.The permeability and the compressive yield stress of fineparticulate solid-liquid systems strongly depend on particle-particle interactions which can be controlled by adjusting thepH and the ionic strength. To investigate the effect of interpar-ticle forces on filtration kinetics and cake structure, the experi-mental determination of the material functions as well asNMR measurements were carried out at different pH values.For characterizing particle-particle interactions the zeta po-tential f was used. According to the DLVO theory, the net in-teraction between particles at high absolute values of the zetapotential (approx. f > 40 mV) is repulsive, at the isoelectricpoint (iep, f = 0) it is attractive [3].2 ExperimentalA fine particulate aqueous alumina suspension was examined(Alcoa, CT 3000 SG, mean particle diameter: 0.6 lm). Thewater used in this study was ion-exchanged and had a conduc-tivity of less than 2 lS/cm. The pH was adjusted using HCland NaOH. Zeta potential measurements were conducted withan Acoustosizer II (Colloidal Dynamics).NMR measurements were carried out with an in situ filtra-tion cell integrated into a NMR tomograph (Bruker Avan-ce 200 SWB) for spin density measurement (1H-NMR), for de-tails, see, e.g., [4].A detailed view of the filtration cell with an outer diameterof 25 mm is given in Fig. 1. The cell is constructed of nonme-tal materials such as PMMA, PVC, and PTFE. As filter medi-um a membrane with 0.2 lm pore diameter was used (Pall,Germany).Fig. 2 shows a schematic drawing of the complete experi-mental setup. The pressure difference was adjusted using avalve and a digital manometer. The filtrate was collected on ahighly accurate balance. Pressure difference and filtrate masswere registered by a computer as a function of time.For the spatially resolved determination of the spin densitya spin-echo pulse sequence based on a work by Horsfield,Fordham and Hall [5] was used (one-dimensional resolutionof 230 lm, absolute measuring time << 1 s). During each fil-tration process a series of one-dimensional NMR scans wasperformed until the end of the consolidation of the filter cakewas reached.The NMR signal was correlated with the solids volume frac-tion in the probe by means of a calibration curve generated bymeasuring the NMR signal of probes with known solids vol-ume fraction. Inhomogeneities of the magnetic field were cor-rected by normalizing the NMR signal with the signal of refer-ence measurements with pure water.The material functions k() and ps() were determinedwith a compression-permeability cell (CP cell).3 Results3.1 Preliminary InvestigationsFirst, filtration experiments within and outside the NMR to-mograph were carried out in order to examine the influence ofthe magnetic field on the filtration behavior of the aluminasuspension. The results showed good agreement, allowing theconclusion that the influence of the magnetic field could beneglected.The relationship between the NMR signal and the solids vol-ume fraction needed for calibration is shown in Fig. 3.The experimentally determined material functions appliedfor the numerical simulation of the filtration processes are pre-© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.comFigure 1. Filter cell for in situ NMR measurements: (1) inlet forpressurized air, (2) lid, (3) filtration ring (PMMA), (4) filter medi-um, (5) support cloth, (6) perforated support plate (PVC), (7) fil-trate outlet, (8) piston (PTFE, optional).Figure 2. Experimental setup for in situ NMR measurements offiltration processes. (1) NMR Tomograph, (2) filter cell, (3)probe head, (4) balance, (5) digital manometer, (6) pressurevalve, (7) air pressure inlet, (8) computer.Chem. Eng. Technol. 2006, 29, No. 7, 828–831 Filtration 829sented in Figs. 4 and 5. Fig. 4 shows the permeability as afunction of the solids volume fraction at two different pH val-ues or zeta potentials. At pH 4 the permeability is much lowerthan at pH 8.6 (see Fig. 10). The dependency of the compres-sive yield stress on the solids volume fraction and the zeta po-tential is illustrated in Fig. 5.Because of the increasing repulsive forces between the parti-cles the network stability decreases with increasing absolutevalue of the zeta potential. This leads to a shift of the functionsps() and k () towards higher solids volume fractions.3.2 Comparison between NMR Data and SimulationResultsFig. 6 shows an experimental result of a filtration process car-ried out within the NMR tomograph at a pressure differenceof 41 kPa, an initial solids volume fraction of 0.095 and a zetapotential of zero (iep, attractive interparticle forces). The solidlines represent lines of constant solids volume fraction. After1000 s the cake height measures 5 mm and the distance be-tween the surface of the remaining suspension and the surfaceof the filter cake is approximately 2 mm. The maximum solidsvolume fraction reached at the bottom of the filter cake is0.38–0.39. Due to the meniscus at the suspension surface theNMR signal does not drop to zero immediately which causesthe presence of several isoconcentration lines in this area (arte-fact).The corresponding simulation result is presented in Fig. 7.Obviously, there is good agreement between the calculated andthe experimentally determined data. The simulation yields a© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.comFigure 3. Calibration curve for correlation of solids volume frac-tion within alumina filter cake and normalized NMR signal.Figure 4. Permeability as a function of solids volume fraction atdifferent zeta potentials (alumina, CP cell measurements).Figure 5. Compressive yield stress as a function of solids volumefraction and zeta potential (alumina, CP cell measurements).Figure 6. NMR measurement: filtration of an alumina suspen-sion at pH 8.6 (iep).Figure 7. Numerical simulation: filtration of an alumina suspen-sion at pH 8.6 (iep).830 A. Erk et al. Chem. Eng. Technol. 2006, 29, No. 7, 828–831cake height of 5.3 mm and a remaining suspension level of2 mm above the cake after a filtration time of 1000 s. Themaximum solids volume fraction reached at the bottom of thefilter cake is 0.4.The results for a zeta potential of 62 mV (highly repulsiveinterparticle forces) are shown in Figs. 8 and 9. NMR data forthe filtration of an alumina suspension at a pressure differenceof 111 kPa and an initial solids volume fraction of 0.117 arepresented in Fig. 8. After 1200 s the cake height measures lessthan 2 mm and the distance between the suspension interfaceand the surface of the filter cake is 15 mm.Fig. 9 shows the simulation data corresponding to the NMRfiltration experiment displayed in Fig. 8. Although there areminor differences concerning cake height and suspension level,simulation and experiment are in good agreement. The calcu-lated maximum solids volume fraction reaches the same valueas in the experiment.The extremely slow cake build-up is caused by the low per-meabilty of the densely packed cake which shows solids vol-ume fractions of up to 0.61. The thin cake layer acts as a bot-tleneck for the suspension above.The high solids volume fraction within the filter cake atf = 62 mV is caused by the repulsive interparticle forces, al-lowing the particles to be arranged in a very close packing (seeFig. 10(B)). If the particle interactions are attractive, a muchmore porous network with a higher permeability is formed,leading to faster filtration rates (see Fig. 10(A)).In conclusion, it can be stated that the applied filtrationmodel combined with the experimentally determined materialfunctions is able to describe the filtration of the investigatedalumina suspension in an accurate way. The strong effects ofvariable interparticle forces on the cake structure and filtrationkinetics were well captured both by NMR measurements andnumerical simulation.AcknowledgementsFinancial support by the DFG (FOR 338) is gratefully acknowl-edged. The authors would like to thank F. Flügel and E. Oliver-Gonzalez for their technical support.Symbols usedI/Iref [–] normalized NMR signalintensityk [m2] permeabilityps [N/m2 = Pa] compressive yield stressDp [N/m2 = Pa] applied pressure difference [–] solids volume fraction0 [–] initial solids volume fractionf [mV] zeta potentialReferences[1] R. Bürger, F. Concha, K. H. Karlsen, Chem. Eng. Sci. 2001,56, 4537.[2] R. Bürger, F. Concha, Int. J. Miner. Process. 2001, 63, 115.[3] Z. Zhou, P. J. Scales, D. V. Boger, Chem. Eng. Sci. 2001, 56,2901.[4] E. H. Hardy, Chem. Eng. Technol. 2006, 29 (7), 785. DOI:10.1002/ceat200600046[5] M. A. Horsfield, E. J. Fordham, L. D. Hall, J. Magn. Reson.1989, 81, 593.© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.comFigure 8. NMR-measurement: filtration of an alumina suspen-sion at pH 4 (f = 62 mV).Figure 9. Numerical simulation: filtration of an alumina suspen-sion at pH 4 (f = 62 mV).Figure 10. Schematic illustration of filter cake microstructure inthe case of attractive (A) and repulsive (B) interparticle interac-tions.Chem. Eng. Technol. 2006, 29, No. 7, 828–831 Filtration 831

Filtration of Colloidal Suspensions - MRI Investigation and Numerical Simulation

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Filtration of Colloidal Suspensions - MRI Investigation and Numerical Simulation

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